Download BLY 303 Lecture Notes, 2012 (O`Brien) III. Population Growth

BLY 303 Lecture Notes, 2012 (O’Brien)
III. Population Growth & Modeling
I. Introduction and Key Concepts
A.
B.
C.
D.
II.
POPULATION ECOLOGY: Study of how and why number of individuals
in a population change over time)
LIFE TABLES: summarize likelihood that individuals within each age
class of population will survive and reproduce
DENSITY INDEPENDENT growth
1.
Changes in size of population do NOT affect growth rate of
population
2.
Described by EXPONENTIAL GROWTH CURVE (J-shaped)
Most populations show DENSITY DEPENDENT growth
1.
Described by a LOGISTIC GROWTH EQUATION that produces a
S-shaped population curve
2.
CARRYING CAPACITY: environment has a maximum number of
individuals that can be supported (represented by K in the logistic
growth equation
Abundance or Population Dynamics
A.
Definitions
1.
Deme
a.
Local population of a single species
b.
A common gene pool
c.
Snails from a single pond
2.
Abundance is the number of individuals
3.
Density
a.
Number of organisms per unit of area, volume or habitat
b.
Generally, small animals are found in higher densities than
big ones
4.
5.
Fecundity is the number of offspring produced by each female
each year
AGE CLASS
a.
Group of individuals of a specific age
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B.
III.
b.
Also referred to as a COHORT
6.
Timing of reproduction
a.
SEMILPAROUS species [SEMEL = one]
(1)
Single reproductive event or “big bang”
(2)
Examples
(a)
Salmon die after spawning
(b)
Many insects such as butterflies and “love
bugs”
b.
ITEROPAROUS species [ITERO = repeat]
(1)
Reproduce many times in life-time
(2)
Primates
(3)
Usually produce small numbers of offspring
Factors that affect abundance
1.
Increase
a.
Natality = births
b.
Immigration = individuals born elsewhere move into deme
2.
Decrease
a.
Mortality = deaths
b.
Emigration = Individuals leave or depart from population
Population Growth Models
A.
Models rely upon mathematical equations
1.
Enable investigators to predict changes in abundance over time
2.
When predictions do not reflect reality, investigators know they do
not understand factors affecting growth of population under study
3.
Important in fisheries management
B.
Types of generations
1.
Discrete generations
a.
Generations do NOT overlap
b.
Examples
(1)
Annual plants
(2)
Most adult insects live less than 1 year
2.
Overlapping generations
a.
Mothers and daughters contribute offspring to the same
generation
b.
Examples
(1)
Trees in hardwood forests
(2)
Long lived mammals
C.
Definitions
1.
∆ is the Greek letter “delta”
a.
In scientific equations, a change in a parameter can be
represented by delta
(1)
∆N = change in number
(2)
∆t = change over time
b.
∆, in turn, is often represented by “d”
(1)
dN = change in number
13
(2)
dt = change in time
2.
RATE
a.
Change in number of individuals over a unit of time
b.
Represented as ∆N / ∆t = dN / dt
3.
r
a.
b.
Intrinsic rate of population change
Instantaneous measure of birth rate minus death rate
at any particular time
r = births - deaths
c.
4.
Significance of values of r
(1)
when r<1, population size is shrinking (births<deaths)
(2)
when r=1, population size remains constant (births =
deaths)
(3)
when r>1, population size is growing (births>deaths)
rmax
a.
D.
The maximum rate of increase for a species occurs when
birth rates are as high as possible and death rates are as
low as possible
b.
Value is assumed to be constant for any one species
c.
Value differs among species
(1)
Relatively high for fish and crabs
(a)
One female produces 100,000s of eggs
(b)
Typical of important fishery species
(2)
Relatively low for large mammals
(a)
Adult females may produce 1 offspring every
other year
(b)
Respond slowly to over harvesting
DENSITY INDEPENDENT growth
1.
Described by exponential or J-shaped curves
2.
Uncontrolled population growth wherein reproduction rate is NOT
influenced by the size of the population [= N]
3.
An ever increasing number of individuals are added to the
population as the size of the population gets larger
4.
The number of individuals added to the population depends upon
N, even when r remains the same
5.
This type of population growth can occur for short intervals when
all resources are available, but it cannot be sustained
6.
Examples:
a.
Organisms colonizing a new habitat
b.
Initial growth of bacteria colonies in a Petri dish
7.
In the real world, as population density increases, r decreases due
to…
a.
Decreases in births due to…
(1)
Malnutrition of females
(2)
Stress
14
b.
Increases in mortality due to…
(1)
Starvation
(2)
Disease
Equation that calculates population size of next generation
8.
N t + 1 = R0N1
wherein
t=
number of the generation or time (age) of the population in
generations
Nt+1 = population size (sometimes just the number of females) at
generation t + 1
Nt
R0
= population size (sometimes # of females) at generation t
= net reproduction rate or the mean number of offspring
produced per individual per generation
Example
R0 = 1.1 and starting or initial population is 100
T (generation)
1
2
3
4
Therefore
R0
(R0 x Nt + 1)
(starting population)
R0 x N1 = 1.1 x 100 =
R0 x N2 = 1.1 x 110 =
R0 x N3 = 1.1 x 121 =
1.1
1.1
1.1
Population size
100
110
121
133.1
N t+1 = R0 N t
N t+2 = R0 N t+1
N t+3 = R0 N t+2
...
…
↓
N t+T = R0 Nt (where T = Number of generations)
800
700
R0 = 1.5
600
N
500
400
300
R0 = 1.1
200
100
1
2
3
4
Generation
15
5
6
E.
DENSITY DEPENDENT growth
1.
Described by LOGISTIC or S-shaped curves
2.
In reality R0 changes with population density
a.
As density increases…
(1)
Increased competition for food and space
(2)
Birth rate decreases
(3)
Increased rates of disease & predation
b.
As density decreases…
(1)
Less competition for food & space
(2)
Birth rate increases
(3)
Decreased exposure to disease and predators
3.
Simple models assume that the relationship between R0 and N is
linear
4.
Logistic, sigmoidal, or S-shaped curves
a.
Describe populations whose growth rate slows as density
increases, in other words, growth becomes densitydependent
The logistic equation
dN/dt = r N [ K - N ]
K
K = upper level (asymptote) to growth = carrying capacity
b.
Carrying capacity
(1)
Represented by “K” in logistic equation
(2)
r slows as population size (= N) approaches K
(3)
Carrying capacity is determined by factors such as:
(a)
Food availability
(b)
Suitable nesting sites
(c)
Disease
(d)
Predation
(4)
Unlike rmax,the carrying capacity of an ecosystem is
not fixed; it can vary from season to season and
year to year
(a)
Winter vs. spring
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(b)
(c)
Example: If r = 1 and K = 100
N
dn/dt
2
1.96
10
9
25
18.75
50
25
5.
IV.
N
75
90
98
Droughts vs. rainy years
Among species
dn/dt
18.75
9
1.96
IMPORTANT POINT: No population can continue to grow
indefinitely
a.
At high densities population growth becomes density
dependent
b.
All populations eventually reach the carrying capacity of
their environment
c.
Reasons why
(1)
Survival varies as a function of population density
(2)
Fecundity varies as a function of population density
Demography
A.
Study of factors that determine the size and structure of populations
through time
B.
Life Tables
1.
Summarize probability than an individual will survive and
reproduce in any given year over the course of its lifetime.
2.
Researchers have been able to capture and mark almost every
individual born into a population of some species and follow each
one over its natural life-span
3.
Data from such studies enable researchers to build life-tables
4.
Example: Study of Lizard Lacerta vivipara
a.
Field collections of marked lizards taken daily
b.
Traced the number of young produced by each individual in
every year of its life
c.
Documented the years when individuals died
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C.
SURVIVORSHIP CURVES
1.
Definition
a.
Data from Life-Tables enable investigators to determine
the proportion of offspring that survive to a particular age
b.
When the percentage of survivors is plotted versus age, a
survivorship curve results
2.
Enable investigators to compare life-history strategies among
species
3.
Types
a.
Type I:
(1)
Survivorship throughout life is high
(2)
Most individuals approach their maximum lifespan
(3)
Examples
(a)
Humans
(b)
Elephants
b.
Type II
(1)
Survivorship (or mortality) is constant throughout
lifetime
(2)
Example: songbirds
c.
Type III
(1)
Mortality is high early in life
(2)
Examples
(a)
Plants
(b)
Parasites
(3)
Oysters
D. The Role of LIFE HISTORY
1.
Defined: How an individual allocates resources to growth,
reproduction, and activities related to survival
2.
Examples
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a.
b.
Relationship between egg size and the number of
eggs a female produces
(1)
A few big eggs
(2)
Many small eggs
Relationship between fecundity and survivorship
(1)
Short-lived species tend to produce high numbers of
eggs
(2)
Long-lived species tend to produce low numbers of
eggs
(3)
Apparently high fecundity AND long survivorship are
not evolutionarily compatible
V.
Age Structure in Human Populations
A.
AGE PYRAMIDS: Graphs with horizontal bars representing the numbers
of males and females of each age group (or year class)
B.
Economically developed countries
1.
Similar numbers of people in most age-classes; age-structure
tends to be even
2.
Exception to above: fewer males than females in older age groups
3.
Political problem: How will older people be cared for if they
outnumber the working population?
C.
Economically undeveloped nations
1.
Populations dominated by young age-classes and individuals
(“bottom-heavy” age pyramid)
2.
Political problem: How to provide education, jobs, and health
care for an enormous percentage of population?
D.
Changes in age structure will have significant impact upon how societies
are organized and what behaviors are acceptable
1. Economic growth
2. Social security
3. Euthanasia
4. Assisted suicide
5. Abortion
E.
Changes in the age structure of human populations
1.
Following the development of the Germ Theory of Disease, child
mortality decreased significantly
2.
The world human population has been increasing at a rate faster
than exponential growth because in cultures typified by poverty,
mothers and daughters have babies concurrently.
Deep Thoughts by Jack O’Brien: Since the “Dawn” of civilization, less than half the
people who ever lived have died (= Over half the people who were ever born are
alive today)
3.
Since 1970, the rate of increase (not the total size) in the world’s
human population has dropped; humans may be experiencing the
first long-term decline in r in their history
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4.
Not everyone believes that the world has a population problem
Quote below is from Howley, K. “The Declining Population,” The
Catholic Week December 30, 1994 p. 6
The facts are: the present population of the world takes up only one percent of the world’s
landspace, and uses less than one-ninth of the earth’s ice-free land to raise food…Famine is
not caused by war and other human defects, not by too many babies. Statistics show that the
current and future food supplies are enough to feed every person in the world, if the residents
of this planet had the will to do it.
Biologist response to above: At what carrying capacity of the world
resources will humans chose to live?
5.
6.
The level of human population in the future depends upon the
FERTILITY RATE: average number of children women have during
their lifetimes
a.
REPLACEMENT RATE
(1)
Each woman produces exactly enough offspring to
replace herself and her offspring’s father
(2)
2.1 children per lifetime
b.
ZERO POPULATION GROWTH (= ZPG)
(1)
r=0
(2)
When replacement rate of 2.1 is sustained for a
generation
In 2002, the United Nations adjusted its projections of human
population growth downward because AIDS significantly increased
the death rate of women in the childbearing ages
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